In music theory, Roman numeral analysis is a type of harmonic analysis in which chords are represented by Roman numerals, which encode the chord's degree and harmonic function within a given musical key.
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. Others use uppercase numerals for all chords regardless of their quality. [2]
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 progression uses the tonic (I), subdominant IV, and dominant (V) chords built upon the first, fourth and fifth scale degrees respectively.
Roman numeral analysis is based on the idea that chords can be represented and named by one of their notes, their root (see History of the Root (chord) article for more information). The system came about initially from the work and writings of Rameau's fundamental bass.
The earliest usage of Roman numerals may be found in the first volume of Johann Kirnberger's Die Kunst des reinen Satzes in 1774. [3] Soon after, Abbé Georg Joseph Vogler occasionally employed Roman numerals in his Grunde der Kuhrpfälzischen Tonschule in 1778. [4] He mentioned them also in his Handbuch zur Harmonielehre of 1802 and employed Roman numeral analysis in several publications from 1806 onwards. [5]
Gottfried Weber's Versuch einer geordneten Theorie der Tonsetzkunst (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. [6] 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. [7] Anton Bruckner, who transmitted the theory to Schoenberg and Schenker, apparently did not use Roman numerals in his classes in Vienna. [8]
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, however, Arabic numerals with carets 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. [9] [10] : 71
Symbol | Meaning | Examples |
---|---|---|
Uppercase Roman numeral | Major triad | I |
Lowercase Roman numeral | Minor triad | i |
Superscript + | Augmented triad | I+ |
Superscript o | Diminished triad | io |
Superscript number | Added note | V7 |
Two or more numbers(#-#) | Figured bass notation | V4–3 |
Superscript # and # # | First inversion | I6 |
Second inversion | I6 4 |
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, "[s]ometimes it is necessary to indicate sharps, flats, or naturals above the bass note." [10] : 74 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 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. [lower-alpha 1]
Roman numerals are sometimes complemented by Arabic numerals to denote inversion of the chords. The system is similar to that of Figured bass, 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 I6
3); the numerals 6
4 denotes the second inversion (e.g. I6
4). 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); V6
5 is its first inversion (B–D–F–G); V4
3 its second inversion (D–F–G–B); and V4
2 or V2 its third inversion (F–G–B–D). [10] : 79–80
In the United Kingdom, there exists another system where the Roman numerals are paired with Latin letters to denote inversion. [13] 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 5
3 is rarely used to denote root position in American nomenclature. [14] [ failed verification – see discussion ] [15] [16] [17]
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:
In popular music and rock music, "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.
The table below shows the Roman numerals for chords built on the major scale.
Scale degree | Tonic | Supertonic | Mediant | Subdominant | Dominant | Submediant | Leading tone |
---|---|---|---|---|---|---|---|
Conventional notation | I | ii | iii | IV | V | vi | viio |
Alternative notation | I | II | III | IV | V | VI | VII [18] |
Chord symbol | I Maj | II min | III min | IV Maj | V Maj (or V7) | VI min | VII dim (or VIIo) |
In the key of C major, these chords are
The table below shows the Roman numerals for the chords built on the natural minor scale.
Scale degree | Tonic | Supertonic | Mediant | Subdominant | Dominant | Submediant | Subtonic | Leading tone |
---|---|---|---|---|---|---|---|---|
Conventional notation | i | iio | ♭III | iv | v | ♭VI | ♭VII | viio |
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 min (or V7) | ♭VI Maj | ♭VII Maj | VII dim (or VIIo) |
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 (V) a major chord (i.e. V major instead of v minor) and the subtonic chord (vii), a diminished chord (viio, instead of ♭VII). This version of minor scale is called the harmonic minor scale. This enables composers to have a dominant chord (V) and also the dominant seventh chord (V7) both available for a stronger cadence resolution in the minor key, thus V to i minor.
In traditional notation, the triads of the seven modern modes are the following:
The major scale 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 double its frequency so that it is called a higher octave of the same note.
In music theory, a leading-tone is a note or pitch which resolves or "leads" to a note one semitone higher or lower, being a lower and upper leading-tone, respectively. Typically, the leading tone refers to the seventh scale degree of a major scale, a major seventh above the tonic. In the movable do solfège system, the leading-tone is sung as ti.
In a musical composition, a chord progression or harmonic progression is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from the common practice era of Classical music to the 21st century. Chord progressions are the foundation of popular music styles, traditional music, as well as genres such as blues and jazz. In these genres, chord progressions are the defining feature on which melody and rhythm are built.
A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor seventh. However, a variety of sevenths may be added to a variety of triads, resulting in many different types of seventh chords.
A chord, in music, is any harmonic set of pitches consisting of multiple notes that are sounded simultaneously, or nearly so. For many practical and theoretical purposes, arpeggios and other types of broken chords may also be considered as chords in the right musical context.
A secondary chord is an analytical label for a specific harmonic device that is prevalent in the tonal idiom of Western music beginning in the common practice period: the use of diatonic functions for tonicization.
In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, was further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.
In music, the submediant is the sixth degree of a diatonic scale. The submediant is named thus because it is halfway between the tonic and the subdominant or because its position below the tonic is symmetrical to that of the mediant above.
In music, function is a term used to denote the relationship of a chord or a scale degree to a tonal centre. Two main theories of tonal functions exist today:
In music, a triad is a set of three notes that can be stacked vertically in thirds. Triads are the most common chords in Western music.
Chromaticism is a compositional technique interspersing the primary diatonic pitches and chords with other pitches of the chromatic scale. In simple terms, within each octave, diatonic music uses only seven different notes, rather than the twelve available on a standard piano keyboard. Music is chromatic when it uses more than just these seven notes.
In music theory, a dominant seventh chord, or major minor seventh chord, is a seventh chord, composed of a root, major third, perfect fifth, and minor seventh. Thus it is a major triad together with a minor seventh, denoted by the letter name of the chord root and a superscript "7". In most cases, dominant seventh chord are built on the fifth degree of the major scale. An example is the dominant seventh chord built on G, written as G7, having pitches G–B–D–F:
The diminished seventh chord is a four-note chord composed of a root note, together with a minor third, a diminished fifth, and a diminished seventh above the root:. For example, the diminished seventh chord built on B, commonly written as Bo7, has pitches B-D-F-A♭:
In music theory, chord substitution is the technique of using a chord in place of another in a progression of chords, or a chord progression. Much of the European classical repertoire and the vast majority of blues, jazz and rock music songs are based on chord progressions. "A chord substitution occurs when a chord is replaced by another that is made to function like the original. Usually substituted chords possess two pitches in common with the triad that they are replacing."
The harmonic minor scale is a 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 seventh degrees.
In music theory, the half-diminished seventh chord is a seventh chord composed of a root note, together with a minor third, a diminished fifth, and a minor seventh. For example, the half-diminished seventh chord built on B, commonly written as Bm7(♭5), or Bø7, has pitches B-D-F-A:
The universal key or universal scale is a concept employed in music theory in which specific notes or chord symbols in a key signature are replaced with numbers or Roman numerals, allowing for a discussion describing relationships between notes or chords that can be universally applied to all key signatures.
In music theory, an inversion is a rearrangement of the top-to-bottom elements in an interval, a chord, a melody, or a group of contrapuntal lines of music. In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory.
Musicians use various kinds of chord names and symbols in different contexts to represent musical chords. In most genres of popular music, including jazz, pop, and rock, a chord name and its corresponding symbol typically indicate one or more of the following:
The jazz minor scale or ascending melodic minor scale is a derivative of the melodic minor scale, except only the ascending form of the scale is used. As the name implies, it is primarily used in jazz, although it may be found in other types of music as well. It may be derived from the major scale with a minor third, making it a synthetic scale, and features a dominant seventh chord on the fifth degree (V) like the harmonic minor scale. It can also be derived from the diatonic Dorian mode with a major seventh.