Roman numeral analysis is an analytical procedure in which musicians use Roman numerals to identify chords within the context of key signatures.

Roman numerals identify the scale degree of the chord's root, the chord's quality, and any extensions or inversions the chord may include.

Uppercase Roman numerals denote major triads, and lowercase Roman numerals denote minor triads. A o symbol after a lowercase Roman numeral represents a diminished triad, while a + sign after an uppercase Roman numeral represents an augmented triad.

The Roman numeral quality of a seventh chord is dependent on the chord's triad; the exceptions are half-diminished and fully diminished seventh chords, whose qualities are dependent on their chordal seventh.

When constructing a chord in SATB style, there are six rules to keep in mind: stem direction, chord construction, range, spacing, voice crossing, and doubling.

Writing Roman Numerals

Music theorists use Roman numerals to identify chords within the context of key signatures. Roman numerals identify the scale degree of the chord's root, the chord's quality, and any extensions or inversions the chord may include. Because Roman numerals convey the same information across major and minor key signatures, using them can save time in analyzing Western common practice music.

The three columns of Example 1 show the Arabic numerals 1 through 7 alongside the corresponding uppercase and lowercase Roman numerals.

Example 1. Arabic and Roman numerals.

To type uppercase Roman numerals, use the uppercase Latin alphabet letters “I” and “V”; likewise, for lowercase Roman numerals, type the lowercase “i” and “v.” The Roman numerals IV (4) and VI (6) are often confused; to remember the difference, think of IV (4) as V minus I (5 minus 1), and VI (6) as V plus I (5 plus 1).

Example 2. The difference between handwritten and typed Roman numerals.

Handwritten uppercase Roman numerals have horizontal bars across the top and bottom of the numeral, in order to further distinguish between uppercase and lowercase (Example 2). There is no such difference with lowercase Roman numerals.

Roman Numerals and Triad Quality

Roman numerals indicate three things: the scale degree of a chord's root, the quality of the chord, and the chord's inversion (see Inversion below). The number represented by the Roman numeral (see Example 1) corresponds to the scale degree of the chord’s root in whatever key the music is in. Uppercase Roman numerals denote major triads, and lowercase Roman numerals denote minor triads. For example, in a major key, a chord built on the first scale degree, \hat1 or do, is identified as “I,” and a chord built on the second scale degree, \hat2 or re, is identified by the lowercase Roman numeral “ii.” Lowercase Roman numerals followed by a superscript "o" (such as viio) represent diminished triads. Uppercase Roman numerals followed by a + sign (for example, the rare V+) represent augmented triads.

In the analysis of Western music, Roman numerals are generally placed below the bottom staff. Some music theorists prefer to use only uppercase Roman numerals, a system which assumes chord quality is intuited; in this textbook, we privilege the distinction of triadic qualities as denoted by uppercase and lowercase Roman numerals.

Example 3 shows the triads and seventh chords of a G major scale, labeled with chord symbols and now Roman numerals (in blue). The solfège and scale degree of the roots are also labeled.

Example 3. Roman numerals of triads in major and minor keys.

The Roman numerals and qualities of triads in major keys are as follows:

I: major

ii: minor

ⅲ: minor

IV: major

V: major

vi: minor

vii°: diminished

The Roman numerals and qualities of triads in minor keys are as follows:

ⅰ: minor

ii°: diminished

III: major

iv: minor

v: minor

V: major (raised leading tone)

VI: major

VII: major

vii°: diminished (raised leading tone)

Note that the quality of v/V and VII/viio differs depending on whether or not the leading tone is raised.

Roman Numerals and Seventh Chord Quality

Roman numeral labels for seventh chords add a superscript 7: for example, V7, ii7, and viio7. The capitalization of the Roman numeral depends on the quality of its triad: uppercase for a major triad (e.g., V7), lowercase for a minor or diminished triad (e.g., ii7). Half-diminished and fully diminished seventh chords, which both contain a diminished triad, are distinguished by an additional symbol after the lowercase Roman numeral: ∅ for half-diminished (e.g., vii∅7) and o for fully diminished (e.g., viio7).

Example 4 shows the triads and seventh chords of a G minor scale labeled with chord symbols and now Roman numerals (in blue). The solfège and scale degree of the roots are also labeled.

Example 4. Roman numerals of seventh chords in major and minor keys.

The Roman numeral and qualities of seventh chords in major keys are as follows:

I7: major-major seventh (major seventh)

ii7: minor-minor seventh (minor seventh)

ⅲ7: minor-minor seventh (minor seventh)

IV7: major-major seventh (major seventh)

V7: major-minor seventh (dominant seventh)

vi7: minor-minor seventh (minor seventh)

vii∅7: half-diminished seventh

The Roman numeral and qualities of seventh chords in minor keys are as follows:

ⅰ7: minor-minor seventh (minor seventh)

ii∅7: half-diminished seventh

III7: major-major seventh (major seventh)

iv7: minor-minor seventh (minor seventh)

v7: minor-minor seventh (minor seventh)

V7: major-minor seventh (dominant seventh)

VI7: major-major seventh (major seventh)

VII7: major-minor seventh (dominant seventh)

vii°7: fully diminished seventh (diminished seventh)

Note that the quality of v7/V7 and VII7/viio7 differs depending on whether or not the leading tone is raised.

Additionally, major seventh and dominant seventh chords have the same Roman numeral nomenclature; in other words, a I7 chord and a V7 chord are written the same even though the former is a major seventh chord and the latter is a dominant seventh c