I. Fundamentals
Roman Numerals
Samuel Brady and Kris Shaffer
Key Takeaways
- Roman numeral analysis is a system of chord labels that contextualize a chord in relation to the overall key of a piece.
- The number represented in the Roman numeral corresponds to the scale degree of the chord’s root.
- If the chord has a seventh, a superscript seven (7) is added to the Roman numeral.
- The quality of a chord is also indicated in Roman numeral analysis:
- Chords with a major third above the root (major, augmented) uses a capital Roman numeral.
- Chords with a minor third above the root (minor, diminished, half-diminished) use a lowercase Roman numeral.
- Special symbols are added for augmented (+), diminished (o), and half-diminished (ø) chords.
Musicians use Roman numerals to identify chords within the context of key signatures. Roman numerals identify the scale degree of the chord’s root ( ). Because Roman numerals are based on scale degrees rather than specific pitch names, they are useful for understanding how harmonies function similarly in different keys.
| Scale degree | Uppercase Roman Numeral | Lowercase Roman Numeral |
|---|---|---|
| 1̂ | I | i |
| 2̂ | II | ii |
| 3̂ | III | iii |
| 4̂ | IV | iv |
| 5̂ | V | v |
| 6̂ | VI | vi |
| 7̂ | VII | vii |
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.”[1] Handwritten uppercase Roman numerals have horizontal bars across the top and bottom of the numeral, in order to further distinguish between uppercase and lowercase ( ). There is no such difference with lowercase Roman numerals.
Roman Numerals and Quality
In addition to showing the chord root, Roman numerals may indicate quality of the chord ([2] 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, [latex]\hat1[/latex] or do, is identified as “I,” a chord built on the second scale degree, [latex]\hat2[/latex] or re, is identified by the lowercase Roman numeral “ii,” and so on. Lowercase Roman numerals followed by a superscript “o” (such as viio) represent diminished triads. Uppercase Roman numerals followed by a + sign (such as V+) represent augmented triads.
).
| Triad quality | Roman numeral characteristics | Example |
|---|---|---|
| major | uppercase | V |
| minor | lowercase | ii |
| augmented | uppercase with + | V+ |
| diminished | lowercase with o | viio |
Just as scale degrees and solfège are the same across keys, so are Roman numerals. shows the Roman numerals for the diatonic triads of G major and G minor as an example, but the same Roman numerals would be used regardless of which pitch is the tonic. The solfège and scale degree of the roots are also labeled—note the correspondence between these and the Roman numerals.
As discussed in previous chapters, if the leading tone is raised in minor, the chord quality changes, and thus the Roman numeral changes: the minor v chord becomes a major V chord, and the subtonic VII chord becomes a diminished viio chord. This means that a Roman numeral in minor sometimes implies a raised leading tone, so remember that when you see a V or a viio in a minor key, you will be using the raised leading tone.
Roman Numerals for Seventh Chords
Roman numeral labels for seventh chords add a superscript 7 (for example, V7, ii7, and viio7). Whether or not the Roman numeral is capitalized depends on the quality: major and dominant seventh chords are capital; minor, diminished, and half-diminished seventh chords are lowercase. As with triads, special symbols are added for augmented and diminished chord qualities: + indicates a seventh chord with an augmented triad, o indicates a fully diminished seventh chord, and ∅ indicates a half-diminished seventh chord. This is summarized in .
| Seventh chord quality | Roman numeral characteristics | Example |
|---|---|---|
| major seventh | uppercase | IV7 |
| dominant seventh | uppercase | V7 |
| minor seventh | lowercase | ii7 |
| half-diminished seventh | lowercase with ∅ | ii∅7 |
| diminished seventh | lowercase with o | viio7 |
Note that major seventh and dominant seventh chords Roman numerals have the same features: a capital Roman numeral followed by a superscript 7. One should infer whether the chord is major or dominant through the key context. Dominant seventh chords are only found on V7 chords (or VII7 in minor); otherwise, assume that a capital Roman numeral with a 7 is a major seventh chord.
shows the seventh chords of the G major and G minor scales, labeled with chord symbols and Roman numerals (in blue). Again, the Roman numerals would be the same for any transposition of these keys.
Roman Numeral Analysis
To complete a Roman numeral analysis, you must first identify the work’s key. A Roman numeral analysis should indicate the key at the beginning of the work or excerpt. As with chord symbols, a capital note name alone indicates major keys, and “mi” would follow to indicate a minor key (e.g., “B♭mi” for B♭ minor). Another common practice is to use lowercase letters for minor keys (e.g., “b♭” for B♭ minor).
Roman numerals are assigned according to the scale degree of each chord’s root, so next, the root must be identified. A chord may be inverted, so the root is not necessarily in the bass. You can re-stack the chord in root position (preferably mentally) if it does not appear that way in the music.
The Roman numeral will be capital or lowercase depending on the chord quality. Because each chord in a key will always have the same quality, you can memorize the qualities of chords within major and minor keys to determine whether the Roman numeral should be capital or lowercase, and whether it needs added special symbols.
To summarize, these are the steps for identifying the Roman numeral of a harmony:
- Identify the key (don’t forget any sharp or flat signs if applicable!).
- Find the root of the chord and note its scale degree. This corresponds to the Roman numeral of the chord.
- Write the Roman numeral, using upper- or lowercase letters and special symbols (if applicable) to show the chord quality.
shows a Roman numeral analysis of “Die Wiese” by Louise Reichardt. Note several features of this analysis:
- The key is labeled at the start of the analysis. Roman numerals are written underneath the staff.
- Roman numerals do not need to be repeated if the chord is not changing.
- Because this piece is in minor, it sometimes uses a raised leading tone (G♯ in A minor), producing major V and dominant V7 chords.
- The unraised G♮ subtonic scale degree produces a dominant seventh chord built on the unraised [latex]\hat7[/latex].[3]
- The A in the vocal part of m. 4 is an embellishing tone—not part of the VII7 harmony and does not affect the Roman numeral.
- This is still a viio7 even though the fifth of the chord is missing.
- Inversion does not change the Roman numeral of a chord.
shows another Roman numeral analysis example. Notes in parentheses are embellishing tones (not part of the harmony).
As seen in
and , several aspects of pitch do not affect the Roman numeral that is assigned to a chord, such as:- Chord voicing, which includes the octave of the notes, doubling of notes, or even the omission of certain notes (especially the chordal fifth).
- Inversion/bass note. Inversion can be shown with figures, as described in the Inversion and Figured Bass chapter, but the Roman numeral does not change.
- Embellishing tones. Not every note in a piece is necessarily considered part of the harmony—sometimes, especially in the melody, notes are better understood as embellishing tones (which you can learn more about in the Embellishing Tones chapter). Embellishing tones may occasionally be indicated with figures, but do not affect a Roman numeral.
Aspects of music outside of pitch—rhythm, timbre, articulation, dynamic, and so on—rarely impact the Roman numeral label of a chord. Because of this, a complete analysis of a piece of music ought to consider more than just the harmonies as understood with Roman numerals. Roman numerals are a helpful tool for describing certain musical phenomena, but they do not tell the whole story.
Roman Numerals and Figures
Roman numerals are often paired with figured bass symbols to denote chord inversions and certain embellishments (Inversion and Figured Bass chapter.
). For example, a superscript 6 represents a first inversion triad, and the figures [latex]^4_3[/latex] would indicate a second inversion seventh chord. This is discussed further in the
- Roman Numeral Analysis: Triads (musictheory.net)
- Harmonizing Scales & Roman Numeral Analysis (Kaitlan Bove)
- Roman Numerals (learnmusictheory.net)
- Roman Numeral Analysis (Phillip Magnuson)
- Roman Numeral Analysis (8notes.com)
- Roman Numeral Chord Symbols (Robert Hutchinson)
- Roman Numerals in Major Flashcards (gmajormusictheory.org)
- Roman Numerals in Minor Flashcards (gmajormusictheory.org)
- Inversion & Roman Numerals in Major Flashcards (gmajormusictheory.org)
- Inversion & Roman Numerals in Minor Flashcards (gmajormusictheory.org)
- How the Roman Numeral System Works (YouTube)
- Roman Numeral Identification, pp. 15–16, 18 (.pdf), pp. 5–7 (.pdf), pp. 1, 3, 4 (.pdf), (.pdf, .pdf, .pdf, .pdf)
- Roman Numeral Identification and Construction, p. 14 (triads) and 17 (seventh chords) (.pdf), p. 11 (.pdf), p. 8 (.pdf), p. 5 (.pdf), (website, website)
- Roman Numeral Construction, p. 22 (.pdf)
- Roman Numerals Identification A (.pdf, .mscz, .mp3). Asks students to create a Roman numeral analysis of a modified Bach chorale.
- Roman Numerals Identification B (.pdf, .mscz, .mp3). Asks students to create a Roman numeral analysis of a modified Bach chorale.
- Roman Numerals Identification C (.pdf, .mscz, .mp3). Asks students to create a Roman numeral analysis of a modified Bach chorale.
- Roman Numerals (.pdf, .mscz). Asks students to identify chord symbols and Roman numerals for open-voicing chords in major and minor keys, realize Roman numerals in closed position, and label the chords of two excerpts with Roman numerals.
Media Attributions
- Handwritten versus typed Roman numerals © Megan Lavengood is licensed under a CC BY-SA (Attribution ShareAlike) license
- The Roman numerals IV (4) and VI (6) are often confused. To remember the difference, think of IV (4) as V minus I (5 − 1 = 4), and VI (6) as V plus I (5 + 1 = 6). ↵
- Some music theorists (especially outside North America) prefer to use only uppercase Roman numerals, a system which assumes chord quality is intuited. ↵
- Another analysis for the VII chord, especially VII7, is as an applied chord in the key of III (V/III). Read more about tonicization and applied chords. ↵
Labeling chords with Roman numerals (and, often, figures).
A single step within a scale; usually indicated by either a solfège syllable or an Arabic numeral with a caret.
The lowest note of a triad or seventh chord when the chord is stacked in thirds.
A term that summarizes the quality of the third, fifth, and seventh (if applicable) above the root of the chord. Common chord qualities are major, minor, diminished, half-diminished, dominant, and augmented.
Numerals I, II, III, IV, V, VI, and VII for 1–7, respectively. In the analysis of harmony, Roman numerals represent triads built on the corresponding scale degree (for example, a V chord is a triad built on 5̂).
1. A scale, mode, or collection that follows the pattern of whole and half steps W–W–H–W–W–W–H, or any rotation of that pattern.
2. Belonging to the local key (as opposed to "chromatic").
The home note or home chord of a scale, or something with the function of that home note.
A 7̂ that is one half step below 1̂. The leading tone is diatonic in major keys, but requires an accidental in minor keys.
A seventh chord whose triad is diminished and whose seventh is diminished.
A seventh chord in which the triad quality is diminished and the seventh quality is minor.
A seventh chord with a major triad and a major seventh.
A seventh chord in which the triad quality is major and the seventh quality is minor.
The act of moving pitch content by a certain interval.
A system of naming chords that specifies the note name of the root, chord quality, and any alterations.
Some basic symbols are given below as a quick reference, but for more detail, see the Chord Symbols chapter.
| chord quality | chord symbol (for a chord with a root of C) |
|---|---|
| major triad | C |
| minor triad | Cmi, Cm, C- |
| diminished triad | Co, Cdim |
| augmented triad | C+, Caug |
| dominant seventh chord | C7 |
| major seventh chord | Cma7, C∆7, Cmaj7 |
| minor seventh chord | Cmi7, C-7, Cm7 |
| half-diminished seventh chord | Cø7, Cm7♭5, C-7♭5 |
| diminished seventh chord | Co7 |
Changing the bass note of a harmony so that, for example, the third is in the bass instead of the root.
An interval of twelve half steps between two notes with the same letter name. The frequencies of two notes related by octave form a 2:1 ratio. Abbreviated “8ve.”
Duplicating some notes of a chord in multiple parts.
Arabic numerals and symbols that indicate intervals above a bass note. These are realized into chords and non-chord tones by musicians.