A Guide to the Circle of Fifths and Why You Should Know Them
If you are new to music theory and/or composing and songwriting, the image above may seem a bit daunting. However once you get used to using it regularly in your playing, improvising, and music writing, it will become a part of your musical vocabulary. The Circle of Fifths is a helpful tool for seeing relationships between keys, chords, and pitches.
What Is The Circle of Fifths?
The Circle of Fifths is a common topic for new music theory students. Images like the one above are often given in music curriculum and printed on posters in music rooms. Even if a musician commits the circle to memory, they aren't sure what to do with it. Many times, musicians simply disregard the Circle of Fifths as tedious theory and fail to see how helpful it is. And it is helpful because the Circle of Fifths shows relationships between pitches, keys, and chords. Our circle uses the color wheel to further illustrate these relationships. We are not going to discuss all of the relationships depicted on the Circle of Fifths in this post, we are going to cover a few of the basics.
The Circle of Fifths shows the relationship between the 12 tones of the chromatic scale. In music theory, we use capital letters to represent major and lowercase letters to represent minor. On our circle, the larger, outer circles represents major keys and the smaller, inner circles represent minor keys. The number of sharps or flats in each of the key signatures are listed next to the minor keys. Since there are 12 chromatic keys, we can discuss the positions of the keys as where they would appear on a clockface.
At the 12 o'clock position, we see "C" in the large red circle and in the smaller pink circle, we see "a". Therefore "C" is a C major and "a" is a minor. You will note that below the a circle, it reads "0 flats, 0 sharps." This is because C major and a minor do not have any flats or sharps in their respective key signatures and in fact, share the same key signature with no flats or sharps. When a major and a minor key share the same key signature, they are called "relative keys." So the relative minor of C major is a minor and the relative major of a minor.
Moving from the 12 o'clock position to the 1 o'clock position, we move up an interval of a perfect fifth, from C (a) to G (e). At 2 o'clock, we move on to D (b), and at 3 o'clock we have A (f♯), and so on. Each time we move up on "hour" on the circle in the clockwise, we add a sharp to (or remove a flat from) the key signature. So at "C", there are no flats or sharps and at "G", we have one sharp and "D" has two. By the time we reach the 5 o'clock position of "B", we have five sharps. We keep adding sharps until we reach C♯ (a♯) at the 7 o-clock position which has seven sharps.
Enharmonic Equivalents
We can also say the B (g♯) is enharmonically equivalent to C♭(a♭) which has seven flats. The next two keys at the 6 and 7 o'clock positions also have enharmonically equivalent keys; G♭ (e♭m) has the enharmonic equivalent is F♯ (d♯m) and C♯ (a♯) has the enharmonic equivalent of D♭ (b♭m).
Looking at a piano key graphic below, you can see the progression by fifths up the piano keyboard spans nearly all 88 keys. For simplicity's sake, our graphic below shows the flatted version of the enharmonic notes only. It is important note that B (g♯), G♭ (e♭m), and D♭ (b♭m) are the generally preferred spellings of these keys. The circle beginning at C and moving clockwise, we find the pitches of C, G, D, A, E, B, F♯/G♭, C♯/D♭, G♯/A♭, D♯/E♭, A♯/B♭, F, and finally we return to C. So the first relationship that the Circle of Fifths shows is ascending perfect fifths.
Now if we start at C and move around the circle counter-clockwise, we move by up by perfect fourths or down by perfect fifths. The pitches moving around the Circle of Fifths counter-clockwise C, F, B♭/A♯, E♭/D♯, A♭/G♯, D♭/C♯, G♭/F♯, B, E, A, D, G, and once again C. Now just as we added a sharp (or removed a flat) with each key signature as we moved around the circle in the clockwise direction, we add a flat or remove a sharp with each successive key signature in the counter-clockwise direction. So our 12 o'clock key of C has no flats or sharps, its neighbor in the counter-clockwise direction is F which has one flat. The next key signature around the circle at 10 o'clock is B♭which has two flats. We keep adding flats with each hour until we reach all seven flats with C♭(a♭), which once again is the enharmonic equivalent to the more commonplace key of B (g♯). When we discuss harmony and chords, we will discuss the fourth and fifth relationships in the circle further.
Another interval that is clearly illustrated on the circle is the tritone. A tritone is the exact middle of an octave, falling between the perfect fifth and perfect fourth. So in "C", the perfect fifth up is G and the perfect fourth up is F; the tritone above C is F♯. The tritone is depicted on the circle b the pitch that is exactly across the circle from it. For example, C is a 12 o'clock and F♯ is located at 6 o'clock. Another example is A which at 3 o'clock has a tritone of E♭directly across the circle from it at 9 o'clock. If you are familiar with color theory, you will also notice that the tritone relationship is illustrated by complimentary colors. For example, C is red and F♯ is green.
There are many other interval and harmonic relationships that are illustrated on the circle that we will not discuss right now but will do so at a later date when we cover intervals and diatonic (in the key) chords in detail.
History
Pythagoras
The Circle of Fifths may look to you like something from Geometry class and that makes a lot of sense. It is geometric. You may have learned about Pythagoras in a Geometry class. He was a Greek philosopher and scholar who lived around 600 B.C.E. and studied the scientific religious, and political ideas. He is said to have come up with the doctrine of Musica Universalis or Music of the Spheres, which states that the planets move according to mathematical equations and resonate together to produce inaudible music.
While exploring proportional relationships with lengths of vibrating string, he stumbled upon the relationships between musical pitches. With this information, he divided the octave into 12 half-step intervals (also called semitones), forming the chromatic scale we still use in Western music today. Musical intervals are the difference in pitch between two sounds. Each half-step inte is equal to 100 cents. He arranged these relationships around a circle forming the Pythagorean Circle, which is divided into 1200 cents. The Pythagorean Circle is the ancestor to the Circle of Fifths we use today.
A note on Pythagorean Theories: Pythagorean theories concerning music and sound were standard on which all Western music scholarship was based for about 2000 years. The woodcut above from 1492, illustrates his ideas about musical proportions and ratios. While his ideas are important, we know today that his theories do not work for all instruments but is true for flutes and strings.
Developments
In 1679, Ukrainian composer and music theorist Nikolay Diletsky took Pythagoras's ideas and created the version you see above and included it in his treatise Idea Grammatika Muskiyskoy, which translstes to "An Idea of Musical Grammar." About 50 years later, in 1728, Baroque German composer and music theorist Johann David Heinichen created a version that added the minor keys as well as the major keys in his treatise, Der Generalbass in der Komposition, which translates as "The Basso Continuo in Composition." There have been many updates and other takes on the circle since then, including the Perennial version which you see at the very top of this post.
Why Learn the Circle of Fifths
Now that we have learned what the Circle of Fifths is and some of its history of the Circle of Fifths, it's time to discuss why you should know them.
1. Major Chord Spelling
We can spell out major and minor chords using the Circle of Fifths. To build a major chord with start with the root note of the chord, then add both a major third and perfect fifth above it. To built a C major chord for example, we first start at 12 o'clock with C, look to the next hour position and find a perfect fifth above it, in this case "G." Then finally, we add the major third above C. To find a major third on the Circle move to the next hour up in the clockwise direction and move to the inner circle and find the relative minor. In this case, we move from the 1 o'clock G to its relative minor or e. So to build a major chord based on C, our spelling is C, E, G. (You can also find major thirds by following the triangles on the circle above.)
2. Minor Chord Spelling
We can built minor chords as well using the circle. A minor chord is built of a minor third and perfect fifth above the root. To find the perfect fifth above a note, more one hour ahead on the clock face. Let's build a minor now based on c. Locate the c minor key on the circle, then move up one hour to find its perfect fifth. In this case that is g. Then look to the relative key to c minor to find the minor third above it. A c minor chord is spelled C, E♭, G.
3. Modulation
When you can clearly see the closely related keys, it becomes easier to modulate between them. Being able to modulate smoothly can be important when you need to transpose or to add harmonic interest to a piece. When you know, the circle you can also anticipate key changes in songs and pieces that you are learning as well as creating.
4. Bass Line Movement
The first reason to know the circle is to create strong, confident bass lines. A very common bass line that is used in many genres of music is the up by a fifth, down by a fourth bass line. For example in the key of G you may have a bass line of G, D, A, E.
5. Chord Progressions
Chord progressions that move using close relationships on the circle leave the most impact. For example, in the key of C the closely related chords are C, G, F (C and its neighbors on the circle) as well as their relative minor of am, em, and dm. We will discuss this more when we cover creating melodies over basic chord progressions.
These are only a few reasons to study the Circle of Fifths, in fact, the more you study it the more relationships you will see. What are some of the other relationships illustrated by the Circle of Fifths?
Further Information and Resources
Music Cents. http://hyperphysics.phy-astr.gsu.edu/hbase/Music/cents.html. (Accessed 1 July 2019).
Music of the Spheres and the Lessons of Pythagoras. http://www.phys.uconn.edu/~gibson/Notes/Section3_7/Sec3_7.htm. (Accessed 1 July 2019).
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