In
music theory
Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...
, Roman numeral analysis is a type of
harmonic analysis
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...
in which
chords
Chord or chords may refer to:
Art and music
* Chord (music), an aggregate of musical pitches sounded simultaneously
** Guitar chord, a chord played on a guitar, which has a particular tuning
* The Chords (British band), 1970s British mod ...
are represented by
Roman numeral
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, ea ...
s, which encode the chord's
degree and
harmonic function
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f\colon U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that i ...
within a given
musical key
In music theory, the key of a piece is the group of pitches, or scale, that forms the basis of a musical composition in Western classical music, jazz music, art music, and pop music.
A particular key features a '' tonic (main) note'' and i ...
.
Specific notation conventions vary: some theorists use uppercase numerals (e.g. I, IV, V) to represent
major chords, and lowercase numerals (e.g. ii, iii, vi) to represent
minor chords
In music theory, a minor chord is a chord that has a root, a minor third, and a perfect fifth. When a chord comprises only these three notes, it is called a minor triad. For example, the minor triad built on A, called an A minor triad, has pit ...
. Others use uppercase numerals for all chords regardless of their
quality
Quality may refer to:
Concepts
*Quality (business), the ''non-inferiority'' or ''superiority'' of something
*Quality (philosophy), an attribute or a property
*Quality (physics), in response theory
*Energy quality, used in various science discipli ...
.
Roger Sessions
Roger Huntington Sessions (December 28, 1896March 16, 1985) was an American composer, teacher, and writer on music. He had started his career writing in a neoclassical style, but gradually moved towards complex harmonies and postromanticism, a ...
(1951). ''Harmonic Practice''. New York: Harcourt, Brace. . p. 7. (As the II, III, and VI chords always are minor chords and the VII always diminished, a further distinguishment is thought unneeded, see table for Major Diatonic scale below)
Roman numerals can be used to notate and analyze the harmonic progression of a composition independent of its specific
key. For example, the ubiquitous
twelve-bar blues
The twelve-bar blues (or blues changes) is one of the most prominent chord progressions in popular music. The blues progression has a distinctive form in lyrics, phrase, chord structure, and duration. In its basic form, it is predominantly ba ...
progression uses the
tonic (I),
subdominant
In music, the subdominant is the fourth tonal degree () of the diatonic scale. It is so called because it is the same distance ''below'' the tonic as the dominant is ''above'' the tonicin other words, the tonic is the dominant of the subdomina ...
(IV), and
dominant (V) chords built upon the first, fourth and fifth scale degrees respectively.
History

Roman numeral analysis is based on the idea that chords can be represented and named by one of their notes, their
root
In vascular plants, the roots are the plant organ, organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often bel ...
(see for more information). The system came about initially from the work and writings of
Rameau
Jean-Philippe Rameau (; ; – ) was a French composer and music theorist. Regarded as one of the most important French composers and music theorists of the 18th century, he replaced Jean-Baptiste Lully as the dominant composer of French opera a ...
's
fundamental bass.
The earliest usage of Roman numerals may be found in the first volume of
Johann Kirnberger
Johann Philipp Kirnberger (also ''Kernberg''; 24 April 1721, Saalfeld – 27 July 1783, Berlin) was a musician, composer (primarily of fugues) and music theorist. He studied the organ with Johann Peter Kellner and Heinrich Nicolaus Gerber, and st ...
's ''Die Kunst des reinen Satzes'' in 1774. Soon after,
Abbé Georg Joseph Vogler
Georg Joseph Vogler, also known as Abbé Vogler (15 June 1749 – 6 May 1814), was a German composer, organist, teacher and theorist. In a long and colorful career extending over many more nations and decades than was usual at the time, Vogler es ...
occasionally employed Roman numerals in his ''Grunde der Kuhrpfälzischen Tonschule'' in 1778. He mentioned them also in his ''Handbuch zur Harmonielehre'' of 1802 and employed Roman numeral analysis in several publications from 1806 onwards.
Gottfried Weber
Jacob Gottfried Weber (1 March 1779 – 21 September 1839) was a German writer on music (especially on music theory), composer, and jurist.
Biography
Weber was born at Freinsheim. From 1824 to 1839, he was the editor of ''Cäcilia'', a musical ...
's ' (''Theory of Musical Composition'') (1817–21) is often credited with popularizing the method. More precisely, he introduced the usage of large capital numerals for major chords, small capitals for minor, superscript
o for diminished 5ths and dashed 7 for major sevenths – see the figure hereby. Simon Sechter, considered the founder of the Viennese "
Theory of the degrees" (''Stufentheorie''), made only a limited use of Roman numerals, always as capital letters, and often marked the fundamentals with letter notation or with Arabic numbers.
Anton Bruckner
Joseph Anton Bruckner (; ; 4 September 182411 October 1896) was an Austrian composer and organist best known for his Symphonies by Anton Bruckner, symphonies and sacred music, which includes List of masses by Anton Bruckner, Masses, Te Deum (Br ...
, who transmitted the theory to
Schoenberg
Arnold Schoenberg or Schönberg (13 September 187413 July 1951) was an Austrian and American composer, music theorist, teacher and writer. He was among the first modernists who transformed the practice of harmony in 20th-century classical music, ...
and
Schenker, apparently did not use Roman numerals in his classes in Vienna.
The first authors to have made a systematic usage of Roman numerals appear to have been
Heinrich Schenker
Heinrich Schenker (19 June 1868 – 14 January 1935) was an Austrian music theory, music theorist #Theoretical writings, whose writings have had a profound influence on subsequent musical analysis. His approach, now termed Schenkerian analysis ...
and
Arnold Schoenberg
Arnold Schoenberg or Schönberg (13 September 187413 July 1951) was an Austrian and American composer, music theorist, teacher and writer. He was among the first Modernism (music), modernists who transformed the practice of harmony in 20th-centu ...
, both in their treatise of harmony.
Common practice numerals
In
music theory
Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...
related to or derived from the
common practice period
In Western classical music, the common practice period (CPP) was the period of about 250 years during which the tonal system was regarded as the only basis for composition. It began when composers' use of the tonal system had clearly supersede ...
, Roman numerals are frequently used to designate
scale degree
In music theory, the scale degree is the position of a particular note on a scale relative to the tonic—the first and main note of the scale from which each octave is assumed to begin. Degrees are useful for indicating the size of intervals ...
s as well as the chords built on them.
In some contexts, however,
Arabic numeral
The ten Arabic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) are the most commonly used symbols for writing numbers. The term often also implies a positional notation number with a decimal base, in particular when contrasted with Roman numerals. ...
s with
caret
Caret () is the name used familiarly for the character provided on most QWERTY keyboards by typing . The symbol has a variety of uses in programming and mathematics. The name "caret" arose from its visual similarity to the original proofre ...
s are used to designate the scale degrees themselves (e.g.
,
,
, ...).
The basic Roman numeral analysis symbols commonly used in pedagogical texts are shown in the table below.
:
The Roman numerals for the seven
root-position diatonic triads built on the notes of the C major scale are shown below.
:
In addition, according to ''Music: In Theory and Practice'', "
metimes it is necessary to indicate sharps, flats, or naturals above the bass note."
[ The accidentals may be below the superscript and subscript number(s), before the superscript and subscript number(s), or using a slash (/) or plus sign (+) to indicate that the interval is raised (either in a flat key signature or a or in a sharp key signature.
]Secondary chords
A secondary chord is an music analysis, analytical label for a specific harmony, harmonic device that is prevalent in the tonality, tonal idiom of Western culture#Music, Western music beginning in the common practice period: the use of Diatonic a ...
are indicated with a slash e.g. V/V.
Modern Schenkerians often prefer the usage of large capital numbers for all degrees in all modes, in conformity with Schenker's own usage.
Inversions
Roman numerals are sometimes complemented by Arabic numerals to denote inversion of the chords. The system is similar to that of Figured bass
Figured bass is musical notation in which numerals and symbols appear above or below (or next to) a bass note. The numerals and symbols (often accidental (music), accidentals) indicate interval (music), intervals, chord (music), chords, and non- ...
, the Arabic numerals describing the characteristic interval(s) above the bass note of the chord, the figures 3 and 5 usually being omitted. The first inversion is denoted by the numeral 6 (e.g. I6 for the first inversion of the tonic triad, even though a complete figuring would require I); the numerals denotes the second inversion (e.g. I). Inverted seventh chords are similarly denoted by one or two Arabic numerals describing the most characteristic intervals, namely the interval of a second between the 7th and the root: V7 is the dominant 7th (e.g. G–B–D–F); V is its first inversion (B–D–F–G); V its second inversion (D–F–G–B); and V or V2 its third inversion (F–G–B–D).
In the United Kingdom, there exists another system where the Roman numerals are paired with Latin letters to denote inversion. In this system, an “a” suffix is used to represent root position, “b” for first inversion, and “c” for second inversion. However, the "a" is rarely used to denote root position, just as is rarely used to denote root position in American nomenclature.
Jazz and pop numerals
In music theory, fake book
A lead sheet or fake sheet is a form of musical notation that specifies the essential elements of a popular song: the melody, lyrics and harmony. The melody is written in modern Western music notation, the lyric is written as text below the s ...
s and lead sheet
A lead sheet or fake sheet is a form of musical notation that specifies the essential elements of a popular song: the melody, lyrics and harmony. The melody is written in modern Western music notation, the lyric is written as text below the s ...
s aimed towards jazz and popular music, many tunes and songs are written in a key, and as such for all chords, a letter name and symbols are given for all triads (e.g., C, G7, Dm, etc.). In some fake books and lead sheets, all triads may be represented by upper case numerals, followed by a symbol to indicate if it is not a major chord (e.g. "m" for minor or "" for half-diminished or "7" for a seventh chord). An upper case numeral that is not followed by a symbol is understood as a major chord. The use of Roman numerals enables the rhythm section
A rhythm section is a group of musicians within a music ensemble or band that provides the underlying rhythm, harmony and pulse of the accompaniment, providing a rhythmic and harmonic reference and "beat" for the rest of the band.
The rhythm ...
performers to play the song in any key requested by the bandleader
A bandleader is the leader of a music group such as a dance band, rock or pop band or jazz quartet. The term is most commonly used with a group that plays popular music as a small combo or a big band, such as one which plays jazz, blues, rhyth ...
or lead singer
The lead vocalist in popular music is typically the member of a group or band whose voice is the most prominent melody in a performance where multiple voices may be heard. The lead singer sets their voice against the accompaniment parts of the ...
. The accompaniment
Accompaniment is the musical part which provides the rhythmic and/or harmonic support for the melody or main themes of a song or instrumental piece. There are many different styles and types of accompaniment in different genres and styles of m ...
performers translate the Roman numerals to the specific chords that would be used in a given key.
In the key of E major, the diatonic chords are:
*Emaj7 becomes Imaj7 (also I∆7, or simply I)
*Fm7 becomes IIm7 (also II−7, IImin7, IIm, or II−)
*Gm7 becomes IIIm7 (also III−7, IIImin7, IIIm, or III−)
*Amaj7 becomes IVmaj7 (also IV∆7, or simply IV)
*B7 becomes V7 (or simply V; often V9 or V13 in a jazz context)
*Cm7 becomes VIm7 (also VI−7, VImin7, VIm, or VI−)
*Dø7 becomes VIIø7 (also VIIm7b5, VII-7b5, or VIIø)
In popular music
Popular music is music with wide appeal that is typically distributed to large audiences through the music industry. These forms and styles can be enjoyed and performed by people with little or no musical training.Popular Music. (2015). ''Fun ...
and rock music
Rock is a Music genre, genre of popular music that originated in the United States as "rock and roll" in the late 1940s and early 1950s, developing into a range of styles from the mid-1960s, primarily in the United States and the United Kingdo ...
, "borrowing" of chords from the parallel minor of a major key is commonly done. As such, in these genres, in the key of E major, chords such as D major (or VII), G major (III) and C major (VI) are commonly used. These chords are all borrowed from the key of E minor. Similarly, in minor keys, chords from the parallel major may also be "borrowed". For example, in E minor, the diatonic chord built on the fourth scale degree is IVm, or A minor. However, in practice, many songs in E minor will use IV (A major), which is borrowed from the key of E major. Borrowing from the parallel major in a minor key, however, is much less common.
Using the V7 or V chord (V dominant 7, or V major) is typical of most jazz and pop music regardless of whether the key is major or minor. Though the V chord is not diatonic to a minor scale, using it in a minor key is not usually considered "borrowing," given its prevalence in these styles.
Diatonic scales
Major scale
The table below shows the Roman numerals for chords built on the major scale
The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at doubl ...
.
:
In the key of C major, these chords are
:
Minor scale
The table below shows the Roman numerals for the chords built on the natural minor scale
In Western classical music theory, the minor scale refers to three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending).
These scales contain all th ...
.
:
In the key of C minor (natural minor), these chords are
:
The seventh scale degree is very often raised a half step to form a leading tone, making the dominant chord
In music, the dominant is the fifth scale degree () of the diatonic scale. It is called the ''dominant'' because it is second in importance to the first scale degree, the tonic. In the movable do solfège system, the dominant note is sung as "So ...
(V) a major chord (i.e. V major instead of v minor) and the subtonic chord (vii), a diminished chord (vii, instead of VII). This version of minor scale is called the harmonic minor scale
The harmonic minor scale (or Aeolian ♮7 scale) is a Scale (music), musical scale derived from the natural minor scale, with the minor seventh degree raised by one semitone to a major seventh, creating an augmented second between the sixth and ...
. This enables composers to have a dominant chord
In music, the dominant is the fifth scale degree () of the diatonic scale. It is called the ''dominant'' because it is second in importance to the first scale degree, the tonic. In the movable do solfège system, the dominant note is sung as "So ...
(V) and also the dominant seventh
Domination or dominant may refer to:
Society
* World domination, structure where one dominant power governs the planet
* Colonialism in which one group (usually a nation) invades another region for material gain or to eliminate competition
* Ch ...
chord (V7) both available for a stronger cadence
In Classical music, Western musical theory, a cadence () is the end of a Phrase (music), phrase in which the melody or harmony creates a sense of full or partial resolution (music), resolution, especially in music of the 16th century onwards.Don ...
resolution in the minor key, thus V to i minor.
:
Modes
In traditional notation, the triads of the seven modern modes are the following:
:
Footnotes
References
{{Musical analysis
Chords
Musical analysis