In music theory, the circle of thirds, also known as the cycle of thirds, is a way of organizing pitches, and a musical tool that helps musicians remember and memorize the order of thirds in a scale, and hence the notes of the chords in those scales. The circle of thirds is not as well known or as versatile as the circle of fifths, but it can still be a valuable concept for musicians to know.[1] For example, the cycle of thirds is inherently important to chord construction, as most triads are built on the cycle of thirds.[2]
Because the circle of thirds is based on the order of thirds in a scale, rather than its ascending scale degrees, the scale degrees of the cycle are in the following order: 1-3-5-7-2-4-6. In the key of C, the order of notes will be C-E-G-B-D-F-A. However, when in another key than C, the order won't start from C, but will still be the same overall order when seen as a circle. For example, for A minor is: A-C-E-G-B-D-F.[1]
The circle of thirds can be played on a standard piano by starting on A0 and playing the sequence of 3-4-3-4... semitone half step intervals or the sequence of 4-3-4-3... semitone half step intervals.
The concept of a "circle of thirds" is relatively new in the history of music. Although certainly not the first to use it, a popular American jazz musician named John Coltrane often used a cycle composed of a sequence of major thirds for his unique key changes, hence the namesake for "coltrane changes". His popularity during the 1960s and in the ensuing decades, brought a lot of attention to the augmented triads, and at the same time, the concept of a cycle of thirds, which was mainly inspired by the "coltrane changes".[3][4]
Although the exact date when the term "circle of thirds" was coined is not known, the circle of thirds and the coltrane changes continue to be used in many jazz compositions to this day, and has extended its reach into other musical genres, such as rock, pop, and other forms of popular music.[4]
The circle of thirds is also mentioned in relation to tonal music, but more rarely.[5]
Structure and modern usage
The C major triad mentioned on the left, as seen in traditional sheet music.
In music, triads are primarily built on the circle of thirds. In fact, by going progressively forward in the repeating 24 note sequence of the circle of thirds, many chords can be constructed.
For example, in A major, the first notes in the cycle of thirds are A, C♯, and E, which is also the three notes present in the A major triad.[2] But this rule not only applies to major or minor chords, but also to seventh chords. For example, in the key in E minor, the tonic chord (E, G, B) becomes an E minor seventh chord (E, G, B, D), if the fourth note (D) is added to the triad. This applies to all other chords in the scale.[1]
A mnemonic also exists in the circle of thirds. The sequence DFACEGB appears three times.
[D♭, F, A♭, C, E♭, G, B♭], [D, F, A, C, E, G, B], [D, F#, A, C#, E, G#, B]
The first sequence of DFACEGB is associated with the major scales and chords commonly notated with flatted notes (D♭, A♭, E♭, B♭) and the third sequence of DFACEGB is associated with the scales and chords that contain sharp notes (D, A, E, B).
Relationship to other scales
The circle of thirds is closely tied to the diatonic scale. Every note on the circle of thirds that starts a minor triad or minor 7th chord starts a sequence of 7 notes that belong to a Dorian scale. For example the sequence DFACEGB in the circle of thirds contains all the notes in D Dorian and D Dorian's associated modes.
Modes Associated with D Dorian
Mode
Notes
D Dorian
D, E, F, G, A, B, C
E Phrygian
E, F, G, A, B, C, D
F Lydian
F, G, A, B, C, D, E
G Mixolydian
G, A, B, C, D, E, F
A Aeolian
A, B, C, D, E, F, G
B Locrian
B, C, D, E, F, G, A
C Ionian
C, D, E, F, G, A, B
Relationship to other circles
The circle of thirds is related to the Circle of fifths. The circle of fifths is composed of the twelve Major keys in the order (C, G, D, A, E, B, F#/G♭, D♭, A♭, E♭, B♭, F) going clockwise. The circle of fifths can also be drawn as a circle of the associated minor keys in the order (Am, Em, Bm, F#m, C#m, G#m, D#m, B♭m, Fm, Cm, Gm, Dm). The circle of thirds is the circle of fifths' Major keys, preceded by each associated minor key.
This cycle of 48 notes represents the first four notes of each major scale, following the order of keys around the circle of fifths.
The jump pattern 15263748... repeating around the circle of thirds will generate a 48 note cycle of modular arithmetic (modulo 12) that groups common tones together.
C, D, E, F, G, A, B, C, D, E, F#, G, A, B, C#, D, E, F#, G#, A, B, C#, D#, E, G♭, A♭, B♭, B, D♭, E♭, F, G♭, A♭, B♭, C, D♭, E♭, F, G, A♭, B♭, C, D, E♭, F, G, A, B♭
This cycle of 48 notes is a sequence of the first four notes of each major scale in the order of fifths from the circle of fifths. This cycle also contains all the Major/Ionian scales (overlapping) in the order of fifths with Dorian, Phrygian and Lydian modes also included for each Major group (e.g. C Ionian, D Dorian, E Phrygian, F Lydian).
In music theory a diatonic scale is a heptatonic (seven-note) scale that includes five whole steps and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps. In other words, the half steps are maximally separated from each other.
In music theory, the term mode or modus is used in a number of distinct senses, depending on context.
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, the key of a piece is the group of pitches, or scale, that forms the basis of a musical composition in Western classical music, art music, and pop music.
Tonality or key: Music which uses the notes of a particular scale is said to be "in the key of" that scale or in the tonality of that scale.
In music, modulation is the change from one tonality to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest. Treatment of a chord as the tonic for less than a phrase is considered tonicization.
Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.
In music theory, the circle of fifths is a way of organizing pitches as a sequence of perfect fifths. Starting on a C, and using the standard system of tuning for Western music, the sequence is: C, G, D, A, E, B, F♯/G♭, C♯/D♭, G♯/A♭, D♯/E♭, A♯/B♭, F, and C. This order places the most closely related key signatures adjacent to one another.
An augmented triad is a chord, made up of two major thirds. The term augmented triad arises from an augmented triad being considered a major chord whose top note (fifth) is raised. When using popular-music symbols, it is indicated by the symbol "+" or "aug". For example, the augmented triad built on A♭, written as A♭+, has pitches A♭-C-E:
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 theory, tertian describes any piece, chord, counterpoint etc. constructed from the intervals of thirds. An interval such as that between the notes A and C encompasses 3 semitone intervals and is termed a minor third while one such as that between C and E encompasses 4 semitones and is called a major third. Tertian harmony principally uses chords based on thirds; the term is typically used to contrast with quartal and quintal harmony which uses chords based on fourths or fifths.
The Dorian mode or Doric mode can refer to three very different but interrelated subjects: one of the Ancient Greek harmoniai ; one of the medieval musical modes; or—most commonly—one of the modern modal diatonic scales, corresponding to the piano keyboard's white notes from D to D, or any transposition of itself.
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.
A heptatonic scale is a musical scale that has seven pitches, or tones, per octave. Examples include:
In music and music theory, a hexatonic scale is a scale with six pitches or notes per octave. Famous examples include the whole-tone scale, C D E F♯ G♯ A♯ C; the augmented scale, C D♯ E G A♭ B C; the Prometheus scale, C D E F♯ A B♭ C; and the blues scale, C E♭ F G♭ G B♭ C. A hexatonic scale can also be formed by stacking perfect fifths. This results in a diatonic scale with one note removed.
In music theory, the harmonic major scale is a musical scale found in some music from the common practice era and now used occasionally, most often in jazz. It corresponds to the Raga Sarasangi in Indian Carnatic music, or Raag Nat Bhairav in Hindustani music.
Jazz chords are chords, chord voicings and chord symbols that jazz musicians commonly use in composition, improvisation, and harmony. In jazz chords and theory, most triads that appear in lead sheets or fake books can have sevenths added to them, using the performer's discretion and ear. For example, if a tune is in the key of C, if there is a G chord, the chord-playing performer usually voices this chord as G7. While the notes of a G7 chord are G–B–D–F, jazz often omits the fifth of the chord—and even the root if playing in a group. However, not all jazz pianists leave out the root when they play voicings: Bud Powell, one of the best-known of the bebop pianists, and Horace Silver, whose quintet included many of jazz's biggest names from the 1950s to the 1970s, included the root note in their voicings.
E is the third note and the fifth semitone of the C major scale, and mi in fixed-do solfège. It has enharmonic equivalents of F♭ [(F-flat) which is by definition a diatonic semitone above E♭] and D, amongst others.
F is a musical note, the fourth above C or fifth below C. It is the fourth note and the sixth semitone of the solfège. It is also known as fa in fixed-do solfège. It is enharmonic equivalent with E♯ (E-sharp) and G, amongst others.
G, also called Sol or So, is the fifth note of the fixed-do solfège starting on C. It is the fifth note and the eighth semitone of the solfège. As such it is the dominant, a perfect fifth above C or perfect fourth below C.
In music, harmonization is the chordal accompaniment to a line or melody: "Using chords and melodies together, making harmony by stacking scale tones as triads".
↑ Meeùs, Nicolas, "Tonal and 'Modal' Harmony: A Transformational Perspective", Keynote address at the Dublin International Conference on Music Analysis, 23 June 2005, online]
Notes
This page is based on this Wikipedia article Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses.
