Roman numeral analysis

Root position triads of the C major scale with Roman numerals.^[1]  Play 

Root position triads of the C natural minor scale with Roman numerals.  Play 

In music, Roman numeral analysis involves the use of Roman numerals to represent chords. In this context, Roman numerals (I, II, III, IV, ...) typically denote scale degrees (first, second, third, fourth, ...). When a Roman numeral is used to represent a chord, it is meant to indicate the scale degree corresponding to its root note, which is the note on which the chord is built. For instance, III is the Roman numeral which denotes either the third degree of a scale, or the chord built on that degree. In many cases, uppercase Roman numerals (such as I, IV, V) represent major chords while lowercase Roman numerals (such as i, iv, v) represent the minor chords (see Major and Minor below for alternative notations); elsewhere, upper-case Roman numerals are used for all chords.^[2] In Western classical music in the 2000s, Roman numeral analysis is used by music students and music theorists to analyze the harmony of a song or piece.

In the most common day-to-day use in pop, rock, traditional music, and jazz and blues, Roman numerals allow musicians to quickly understand the progression of chords in a song. For instance, the standard twelve bar blues progression is denoted by the Roman numerals I (first), IV (fourth), and V (fifth), which is sometimes written I7, IV7 and V7, since the blues progression is often based on dominant seventh chords. In the key of C (where the notes of the scale are C, D, E, F, G, A, B), the first scale degree (Tonic) is C, the fourth (Subdominant) is F, and the fifth (Dominant) is a G. So the I7, IV7, and V7 chords are C7, F7, and G7. Similarly, if one were to play the same progression in the key of A (A, B, C♯, D, E, F♯, G♯) the I7, IV7, and V7 chords would be A7, D7, and E7. In essence, Roman numerals provide a way to abstract chord progressions, by making them independent of the selected key. This allows chord progressions to be easily transposed by backup band musicians or rhythm section players to any key.

Overview

Roman numeral analysis is the use of Roman numeral symbols in the musical analysis of chords. In music theory related to or derived from the common practice period, Roman numerals are frequently used to designate scale degrees as well as the chords built on them.^[2] In some contexts, arabic numerals with carets are used to designate scale degrees (); theory related to or derived from jazz or modern popular music may use Roman numerals or arabic numbers (1, 2, 3, etc...) to represent scale degrees (See also diatonic function). In some contexts an arabic number, or careted number, may refer also to a chord built upon that scale degree. For example, $\hat 1$ or 1 may both refer to the chord upon the first scale step.

Gottfried Weber's Versuch einer geordneten Theorie der Tonsetzkunst (Theory of Musical Composition) (Mainz, B. Schott, 1817–21) is credited with popularizing the analytical method by which a chord is identified by the Roman numeral of the scale-degree number of its root. However, the practice originated in the works of Abbé Georg Joseph Vogler, whose theoretical works as early as 1776 employed Roman numeral analysis.^[3]

Common practice numerals

Types of triads:  I ,  i ,  i^o ,  I⁺ 

Roman numeral analysis symbols[4][5]
Symbol	Meaning	Examples
Uppercase Roman numeral	Major triad	I
Lowercase Roman numeral	Minor triad	i
Superscript °	Diminished triad	i°
Superscript ^+ (sometimes ^x )	Augmented triad	I^+
Superscript number	added note	V^7, I^6
Two or more numbers	figured bass notation	V^4 - 3, I6 4 (equivalent to Ic)
Lowercase b	First inversion	Ib
Lowercase c	Second inversion	Ic
Lowercase d	Third inversion	V^7d

The current system used today to study and analyze tonal music comes about initially from the work and writings of Rameau’s fundamental bass. The dissemination of Rameau’s concepts could only have come about during the significant waning of the study of harmony for the purpose of the basso continuo and its implied improvisational properties in the later 18th century. The use of Roman numerals in describing fundamentals as “scale degrees in relation to a tonic” was brought about, according to one historian, by John Trydell’s Two Essays on the Theory and Practice of Music, published in Dublin in 1766.^[6] However, another source says that Trydell used Arabic numerals for this purpose, and Roman numerals were only later substituted by Georg Joseph Vogler.^[7] Alternatives include the functional hybrid Nashville number system^[8] and macro analysis.

Jazz and pop numerals

In music theory, fake books and lead sheets 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, d-, 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. "-" for minor or "ø" 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 performers to play the song in any key requested by the bandleader or lead singer. The accompaniment 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:

• E maj⁷ becomes I maj⁷ (or simply I)
• F♯ -⁷ becomes ii -⁷ (or simply ii)
• G♯ -⁷ becomes iii -⁷ (or simply iii)
• A maj⁷ becomes IV maj⁷ (or simply IV)
• B⁷ becomes V⁷ (or simply V)
• C♯ -⁷ becomes vi -⁷ (or simply vi)
• D♯^ø7 becomes vii^ø7 (or simply vii)

In popular music and rock music, "borrowing" of chords from the tonic minor of a key into the tonic major and vice versa 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. As well, in minor keys, chords from the tonic major may also be "borrowed". For example, in e minor, the diatonic chords for the iv and v chord would be a minor and b minor; in practice, many songs in e minor will use IV and V chords (A major and B major), which are "borrowed" from the key of E Major.

Major

Scale degree (major mode)	Tonic	Supertonic	Mediant	Subdominant	Dominant	Submediant	Leading tone
Traditional notation	I	ii	iii	IV	V	vi	vii^°
Alternative notation	I	II	III	IV	V	VI	VII[9]
Chord symbol	I Maj	II min	III min	IV Maj	V Maj (or V7)	VI min	VII dim (or VII^°)

Minor

Scale degree (minor mode)	Tonic	Supertonic	Mediant	Subdominant	Dominant	Submediant	Subtonic	Leading tone
Traditional notation	i	ii^°	III	iv	V	VI	VII	vii^°
Alternative notation	I	ii	iii	iv	v	vi	vii
Chord symbol	I min	II dim	♭III Aug (or III Maj)	IV min (or IV Maj)	V Maj (or V7)	♭VI Maj	♭VII Maj	VII dim (or VII^°)

Sources

1. Jonas, Oswald (1982). Introduction to the Theory of Heinrich Schenker (1934: Das Wesen des musikalischen Kunstwerks: Eine Einführung in Die Lehre Heinrich Schenkers), p.22. Trans. John Rothgeb. ISBN 0-582-28227-6. Shown all uppercase.
2. Sessions, Roger (1951). Harmonic Practice. New York: Harcourt, Brace. LCCN 51008476. p. 7.
3. Floyd Kersey Grave and Margaret G. Grave, In Praise of Harmony: The Teachings of Abbé Georg Joseph Vogler (1988).
4. Bruce Benward & Marilyn Nadine Saker (2003), Music: In Theory and Practice, seventh edition, 2 vols. (Boston: McGraw-Hill) Vol. I, p. 71. ISBN 978-0-07-294262-0.
5. Taylor, Eric (1989). The AB Guide to Music Theory, Part 1. London: Associated Board of the Royal Schools of Music. ISBN 1-85472-446-0. pp. 60–61.
6. Dahlhaus, Carl. "Harmony." Grove Online Music Dictionary
7. Richard Cohn, "Harmony 6. Practice". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001).
8. Gorow, Ron (2002). Hearing and Writing Music: Professional Training for Today's Musician, second edition (Studio City, California: September Publishing, 2002), p. 251. ISBN 0-9629496-7-1.
9. Mehegan, John (1989). Jazz Improvisation 1: Tonal and Rhythmic Principles (Revised and Enlarged Edition) (New York: Watson-Guptill Publications, 1989), pp. 9-16. ISBN 0-8230-2559-4.