For scale-step in Schenkerian analysis, see scale-step.
In music theory, scale degree refers to 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 and chords, and whether they are major or minor.
In the most general sense, the scale degree merely is the number given to each step of the scale, usually starting with 1=tonic. Defining it like this implies that a tonic is specified. For instance the 7-tone diatonic scale may become the major scale once the proper degree has been chosen as tonic (e.g. the C-major scale C–D–E–F–G–A–B, in which C is the tonic). If the scale has no tonic, the starting degree must be chosen arbitrarily. In set theory, for instance, the 12 degrees of the chromatic scale usually are numbered starting from C=0, the twelve pitch classes being numbered from 0 to 11.
In a more specific sense, scale degrees are given names that indicate their particular function within the scale. This definition implies a functional scale, as is the case in tonal music.
The expression scale step is sometimes used synonymously with scale degree, but it may alternatively refer to the distance between two successive and adjacent scale degrees (see Steps and skips). The terms "whole step" and "half step" are commonly used as interval names (though "whole scale step" or "half scale step" are not used). The number of scale degrees and the distance between them together define the scale they are in.
Major and minor scales
The degrees of the traditional major and minor scales may be identified several ways:
- the first, second, (major or minor) third, fourth, fifth, major or minor sixth, and major or minor seventh degrees of the scale;
- by Arabic numerals (1, 2, 3, 4 ...), sometimes with circumflexes ();
- by Roman numerals (I, II, III, IV ...);
- the diatonic mode which starts on the degree, and contains all the notes in the key
- in English, by the names and function: tonic, supertonic, mediant, subdominant, dominant, submediant, leading note (leading tone in the United States) and tonic again.
- These names are derived from a scheme where the tonic note is the 'center'. Supertonic and subtonic are, respectively, one step above and one step below the tonic; mediant and submediant are each a third above and below the tonic, and dominant and subdominant are a fifth above and below the tonic.
- Subtonic is used when the interval between it and the tonic in the upper octave is a whole step; leading note when that interval is a half-step.
- in English, by the "moveable Do" Solfege system, which allows a person to name each scale degree with a single syllable while singing.
|Degree||Name (Diatonic Function)||Corresponding mode (major key)||Corresponding mode (minor key)||Meaning||Note (in C major)||Note (in C minor)|
|1st||Tonic||Ionian||Aeolian||Tonal center, note of final resolution||C||C|
|2nd||Supertonic||Dorian||Locrian||One whole step above the tonic||D||D|
|3rd||Mediant||Phrygian||Ionian||Midway between tonic and dominant, (in minor key) root of relative major key||E||E♭|
|4th||Subdominant||Lydian||Dorian||Lower dominant, same interval below tonic as dominant is above tonic||F||F|
|5th||Dominant||Mixolydian||Phrygian||2nd in importance to the tonic||G||G|
|6th||Submediant||Aeolian||Lydian||Lower mediant, midway between tonic and subdominant, (in major key) root of relative minor key||A||A♭|
|7th||Leading tone(in Major scale) / Subtonic (in Natural Minor Scale)||Locrian||Mixolydian||Melodically strong affinity for and leads to tonic/One half step below tonic in Major scale and whole step in Natural minor.||B||B♭|
|1st (8th)||Tonic (octave)||Ionian||Aeolian||Tonal center, note of final resolution||C'||C'|
- ^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.
- ^Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.32-3. Seventh Edition. ISBN 978-0-07-294262-0. "Scale degree names: Each degree of the seven-tone diatonic scale has a name that relates to its function. The major scale and all three forms of the minor scale share these terms."
- ^Kolb, Tom (2005). Music Theory for Guitarists, p.16. ISBN 0-634-06651-X.
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. 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.
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. 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, 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.
Common practice numerals
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. However, another source says that Trydell used Arabic numerals for this purpose, and Roman numerals were only later substituted by Georg Joseph Vogler. Alternatives include the functional hybrid Nashville number system and macro analysis.
Jazz and pop numerals
Main article: Universal key
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:
- E7 becomes I7 (or simply I)
- F♯m7 becomes ii7 (or simply ii)
- G♯m7 becomes iii7 (or simply iii)
- A7 becomes IV7 (or simply IV)
- B7 becomes V7 (or simply V)
- C♯m7 becomes vi7 (or simply vi)
- D♯ø7 becomes viiø7 (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.
|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 VIIo)|
In traditional notation, the triads of the seven modes are the following:
|Mode||Tonic||Supertonic||Mediant||Subdominant||Dominant||Submediant||Subtonic / Leading tone|
|6.||Aeolian (natural minor)||i||iio||♭III||iv||v||♭VI||♭VII|
- ^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.
- ^ abSessions, 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.