# Circle of thirds

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. For example, the cycle of thirds is inherently important to chord construction, as most triads are built on the cycle of thirds.
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.
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.

## History
### Origins

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".
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.
The circle of thirds is also mentioned in relation to tonal music, but more rarely.

## Structure and modern usage
### Chord construction

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.
F#/G♭–b♭–D♭–f–A♭–c–E♭–g–B♭–d–F–a–C–e–G–b–D–f#–A–c#–E–g#–B–d#–F#/G♭
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. 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.
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.
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).