Roman numeral analysis

In music, Roman numeral analysis uses Roman numerals to represent chords. The Roman numerals (I, II, III, IV, ...) denote scale degrees (first, second, third, fourth, ...); used to represent a chord, they denote the root note on which the chord is built. For instance, III denotes the third degree of a scale or the chord built on it. Generally, uppercase Roman numerals (such as I, IV, V) represent major chords while lowercase Roman numerals (such as i, iv, v) represent 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 notate the progression of chords in a song. For instance, the standard twelve bar blues progression is I (first), IV (fourth), V (fifth), sometimes written I⁷, IV⁷, 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. In 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. Roman numerals thus abstract chord progressions, making them independent of the key, so can easily be transposed.

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 ();^{[citation needed]} 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.^{[citation needed]} For example, or 1 may both refer to the chord upon the first scale step.^{[citation needed]}

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.^{[citation needed]} 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

Roman numeral analysis symbols^[4]^[5]
Symbol	Meaning	Examples
Uppercase Roman numeral	Major triad	I
Lowercase Roman numeral	Minor triad	i
Superscript ^o	Diminished triad	i^o
Superscript ⁺ (sometimes ^x ^{[citation needed]})	Augmented triad	I⁺
Superscript number	added note	V⁷, I⁶
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	V⁷d

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, 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 "^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:

Emaj⁷ becomes Imaj⁷ (or simply I)
F♯m⁷ becomes ii⁷ (or simply ii)
G♯m⁷ becomes iii⁷ (or simply iii)
Amaj⁷ becomes IVmaj⁷ (or simply IV)
B⁷ becomes V⁷ (or simply V)
C♯m⁷ becomes vi⁷ (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

Western Major Scale Natural Chords
Scale degree (major mode)	Tonic	Supertonic	Mediant	Subdominant	Dominant	Submediant	Leading tone
Traditional notation	I	ii	iii	IV	V	vi	vii^o
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^o)

Minor

Western Natural Minor Scale’s Natural Chords
Scale degree (minor mode)	Tonic	Supertonic	Mediant	Subdominant	Dominant	Submediant	Subtonic	Leading tone
Traditional notation	i	ii^o	♭III	iv	V	♭VI	♭VII	vii^o
Alternative notation	I	ii^{[citation needed]}	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^o)

Modes

In traditional notation, the triads of the seven modes are the following:

Modal Natural Chords
	Mode	Tonic	Supertonic	Mediant	Subdominant	Dominant	Submediant	Subtonic / Leading tone
1.	Ionian (major)	I	ii	iii	IV	V	vi	vii^o
2.	Dorian	i	ii	♭III	IV	v	vi^o	♭VII
3.	Phrygian	i	♭II	♭III	iv	v^o	♭VI	♭vii
4.	Lydian	I	II	iii	♯iv^o	V	vi	vii
5.	Mixolydian	I	ii	iii^o	IV	v	vi	♭VII
6.	Aeolian (natural minor)	i	ii^o	♭III	iv	v	♭VI	♭VII
7.	Locrian	i^o	♭II	♭iii	iv	♭V	♭VI	♭vii

Sources

^ 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.
^ ^a ^b Sessions, Roger (1951). Harmonic Practice. New York: Harcourt, Brace. LCCN 51-8476. p. 7.
^ Floyd Kersey Grave and Margaret G. Grave, In Praise of Harmony: The Teachings of Abbé Georg Joseph Vogler (1988).^{[full citation needed]}
^ 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.
^ 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.
^ Dahlhaus, Carl. "Harmony." Grove Online Music Dictionary
^ 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).
^ 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.
^ 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.

[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.

[roger-2] Sessions, Roger (1951). Harmonic Practice. New York: Harcourt, Brace. LCCN 51-8476. p. 7.

[3] Floyd Kersey Grave and Margaret G. Grave, In Praise of Harmony: The Teachings of Abbé Georg Joseph Vogler (1988).^{[full citation needed]}

[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.

[eric-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.

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