The symbols (C, Db, ...) on the diagram can be thought of in three ways:
1) as notes, specifically, the twelve semitones or notes of the octave (C means the note C on the piano or any instrument); or
2) as chords (C means the C major chord: C-E-G); or
3) as keys (C means the diatonic key of C major, which is the familiar tune do re me fa so la ti do with C playing the role of do).
1) As notes: Think of the letters as the twelve tones that make up an octave (all the piano keys in an octave, the white ones and the black ones). Move around the circle clockwise, starting at C. Each succeeding note is an interval of a perfect fifth (seven semitones) above the previous one (G is a fifth above C). Start at C and move counterclockwise. Each succeeding note is an interval of a perfect fifth below the previous one (F is a fifth below C).
This is the simplest reason for calling the diagram the circle of fifths. You can see that the diagram encodes the relationships among all the intervals of a fifth within the twelve-tone octave.
That's not all it encodes. Again moving clockwise, each succeeding note is also an interval of a perfect fourth (five semitones) below the previous one (G is a fourth below C); and again moving counterclockwise, each succeeding note is a perfect fourth above the previous one (F is a fourth above C).
We are just starting to see some of what the circle of fifths gives us.
3) As chords: Think of C as the C major chord, C-E-G (in intervals, the 1-3-5 chord). Move once clockwise, and you reach the G chord (G-B-D), which is the dominant chord in the key of C. Or start at C, move once counterclockwise, and you reach the F chord (F-A-C), which is the subdominant chord in the key of C. All three of these chords contain only notes in the C major scale (the white keys on the piano), and hence they harmonize nicely with any tune on that scale. So C is surrounded by its subdominant (F) and dominant (G) chords. Many simple songs require only these three chords -- the tonic, the dominant, and the subdominant -- for harmonic accompaniment:
C G C G
The gypsy rover came over the hill,
C G C G
and down in the valley so sha - dy.
C G C F
He whistled and he sang till the greenwood rang,
C G C F C G
and he won the heart of a la --- dy.
Another important chord in some songs is the relative minor chord, consisting of the tonic, the flatted third, and the dominant (in intervals, the 1-3b-5 chord). For the key of C, the relative minor chord is A minor: A-C-E. As with the G and F chords, these are all white-key notes, so this chord is also very consonant with the scale in C. Notice that A is 3 steps, or one quarter of the circle, clockwise from C.
C Am F G
Somewhere, beyond the sea,
This relationship, in which nearest neighbors are the subdominant and dominant chords, and the chord 1/4 of the way around clockwise is the relative minor chord, holds for any chord on the diagram. If you want to play The Gypsy Rover in any other key, say E, the circle of fifths makes it easy to find the dominant and subdominant chords for the key of E: B and A, respectively. Simply substitute these chords for the ones shown (and sing higher!). Question: In the key of E, what is the relative minor chord? (Answer: Db or its identical twin, C#)
As keys: If the think of the letters as keys, then the circle of fifths shows which keys have diatonic scales with the most notes in common. The nearer two keys are to each other on the circle, the more notes their scales have in common. For example, the diatonic scale in C has no sharps and flats, it consists of all the white keys on the piano. Its neighbors are the key of F (which has one black key, Bb) and the key of G (one black key, F#). The key of Bb, two keys counterclockwise from C, has two flats; the key of D, two keys clockwise from C, has two sharps. The number of differences between two keys would be the same for any key you pick -- one difference if they are nearest neighbors, two differences if they are two positions apart, and so forth. Two keys on opposite sides of the circle, say, A and Eb, have the minimum number of notes in common.
In classical music, one very common way to change the key of a melody is to let the dominant chord in the current key become the tonic for the melody, thus shifting the melody up or down by a perfect fifth.
This version of the circle of fifths shows more about each key.
This is just a glimpse of the relationships that the circle of fifths encodes.
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In the following video about harmony, Leonard Bernstein shows how the gradual introduction of new harmonies changed music over hundreds of years, and how music would sound at each stage. In addition he shows how Bach used fifths to build the twelve-tone octave and make possible harmonically pleasing movement among different keys, all made of compatible diatonic scales. Also implied is the main reason that the modern octave has twelve tones.
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In the following video, Michael New tells more about how musicians and composers make practical use of the circle of fifths.
For more of Michael's lessons in music theory, click his name above.
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